Maximal time regularity for degenerate evolution integro-differential equations
β Scribed by Alberto Favaron; Angelo Favini
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 470 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1424-3199
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## Abstract We consider nonlinear integroβdifferential equations like the ones that arise from stochastic control problems with purely jump LΓ©vy processes. We obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior __C__^1, Ξ±^ regularity for general fully nonlinear integroβd
A ΠΈ g C 0, T , L L D A 0 , X and construct the corresponding evolution family on the underlying Banach space X. Our proofs are based on the operator sum method and the use of evolution semigroups. The results are applied to parabolic partial differential equations with continuous coefficients.
Time point relaxation methods based on direct quadrature methods and on Runge-Kutta methods for the numerical solution of Volterra integro-differential systems are proposed. The convergence of the discrete-time iterations is analyzed. (~